@article{0266-5611-34-11-114001,
author={Christine Grathwohl and Peer Kunstmann and Eric Todd Quinto and Andreas Rieder},
title={Microlocal analysis of imaging operators for effective common offset seismic reconstruction},
journal={Inverse Problems},
volume={34},
number={11},
pages={114001},
url={http://stacks.iop.org/0266-5611/34/i=11/a=114001},
year={2018},
abstract={The elliptic Radon transform (eRT) integrates functions over ellipses in 2D and ellipsoids of revolution in 3D. It thus serves as a model for linearized seismic imaging under the common offset scanning geometry where sources and receivers are offset by a constant vector. As an inversion formula of eRT is unknown we propose certain imaging operators (generalized backprojection operators) which allow to reconstruct some singularities of the searched-for reflectivity function from seismic measurements. We calculate and analyze the principal symbols of these imaging operators as pseudo-differential operators to understand how they map, emphasize or de-emphasize singularities. We use this information to develop local reconstruction operators that reconstruct relatively independently of depth and offset. Numerical examples illustrate the theoretical findings.}
}